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Register a new userFar-Infrared Photometric Redshifts: A New Approach to a Highly Uncertain Enterprise
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Caitlin M. Casey
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I present a new approach at deriving far-infrared photometric redshifts for galaxies based on their reprocessed emission from dust at rest-frame far-infrared through millimeter wavelengths. Far-infrared photometric redshifts (FIR-$z$) have been used over the past decade to derive redshift constraints for highly obscured galaxies that lack photometry at other wavelengths like the optical/near-infrared. Most literature FIR-z fits are performed through $chi^2$minimization to a single galaxys far-infrared template spectral energy distribution (SED). The use of a single galaxy template, or modest set of templates, can lead to an artificially low uncertainty estimate on FIR-$z$s because real galaxies display a wide range in intrinsic dust SEDs. I use the observed distribution of galaxy SEDs (for well-constrained samples across $0<z<5$) to motivate a new far-infrared through millimeter photometric redshift technique called MMpz. The MMpz algorithm asserts that galaxies are most likely drawn from the empirically observed relationship between rest-frame peak wavelength, $lambda_{rm peak}$, and total IR luminosity, L$_{rm IR}$; the derived photometric redshift accounts for the measurement uncertainties and intrinsic variation in SEDs at the inferred L$_{rm IR}$, as well as heating from the CMB at $z>5$. The MMpz algorithm has a precision of $sigma_{Delta z/(1+z)}approx0.3-0.4$, similar to single-template fits, while providing a more accurate estimate of the FIR-$z$ uncertainty with reduced chi-squared of order $mathcal{O}(chi^2_{ u})=1$, compared to alternative far-infrared photometric redshift techniques (with $mathcal{O}(chi^2_{ u})approx10-10^{3}$).
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We introduce a new effective strategy to assign group and cluster membership probabilities $P_{mem}$ to galaxies using photometric redshift information. Large dynamical ranges both in halo mass and cosmic time are considered. The method takes the magnitude distribution of both cluster and field galaxies as well as the radial distribution of galaxies in clusters into account using a non-parametric formalism and relies on Bayesian inference to take photometric redshift uncertainties into account. We successfully test the method against 1,208 galaxy clusters within redshifts $z=0.05-2.58$ and masses $10^{13.29-14.80}~M_odot$ drawn from wide field simulated galaxy mock catalogs developed for the Euclid mission. Median purity $(55^{+17}_{-15})%$ and completeness $(95^{+5}_{-10})%$ are reached for galaxies brighter than 0.25$L_ast$ within $r_{200}$ of each simulated halo and for a statistical photometric redshift accuracy $sigma((z_s-z_p)/(1+z_s))=0.03$. The mean values $p=56%$ and $c=93%$ have sub-percent uncertainties. Accurate photometric redshifts ($sigma((z_s-z_p)/(1+z_s))lesssim0.05$) and robust estimates for the cluster redshift and the center coordinates are required. The method is applied to derive accurate richness estimates. A statistical comparison between the true ($N_{rm true}$) vs estimated richness ($lambda=sum P_{mem}$) yields on average to unbiased results, $Log(lambda/N_{rm true})=-0.0051pm0.15$. The scatter around the mean of the logarithmic difference between $lambda$ and the halo mass is 0.10~dex, for massive halos $gtrsim10^{14.5}~M_odot$. Our estimates could be useful to calibrate independent cluster mass estimates from weak lensing, SZ, and X-ray studies. Our method can be applied to any list of galaxy clusters or groups in both present and forthcoming surveys such as SDSS, CFHTLS, DES, LSST, and Euclid.
Based on the SDSS and SDSS-WISE quasar datasets, we put forward two schemes to estimate the photometric redshifts of quasars. Our schemes are based on the idea that the samples are firstly classified into subsamples by a classifier and then photometric redshift estimation of different subsamples is performed by a regressor. Random Forest is adopted as the core algorithm of the classifiers, while Random Forest and kNN are applied as the key algorithms of regressors. The samples are divided into two subsamples and four subsamples depending on the redshift distribution. The performance based on different samples, different algorithms and different schemes are compared. The experimental results indicate that the accuracy of photometric redshift estimation for the two schemes generally improve to some extent compared to the original scheme in terms of the percents in frac{|Delta z|}{1+z_{i}}<0.1 and frac{|Delta z|}{1+z_{i}}<0.2 and mean absolute error. Only given the running speed, kNN shows its superiority to Random Forest. The performance of Random Forest is a little better than or comparable to that of kNN with the two datasets. The accuracy based on the SDSS-WISE sample outperforms that based on the SDSS sample no matter by kNN or by Random Forest. More information from more bands is considered and helpful to improve the accuracy of photometric redshift estimation. Evidently it can be found that our strategy to estimate photometric redshift is applicable and may be applied to other datasets or other kinds of objects. Only talking about the percent in frac{|Delta z|}{1+z_{i}}<0.3, there is still large room for further improvement in the photometric redshift estimation.
Upcoming imaging surveys, such as LSST, will provide an unprecedented view of the Universe, but with limited resolution along the line-of-sight. Common ways to increase resolution in the third dimension, and reduce misclassifications, include observing a wider wavelength range and/or combining the broad-band imaging with higher spectral resolution data. The challenge with these approaches is matching the depth of these ancillary data with the original imaging survey. However, while a full 3D map is required for some science, there are many situations where only the statistical distribution of objects (dN/dz) in the line-of-sight direction is needed. In such situations, there is no need to measure the fluxes of individual objects in all of the surveys. Rather a stacking procedure can be used to perform an `ensemble photo-z. We show how a shallow, higher spectral resolution survey can be used to measure dN/dz for stacks of galaxies which coincide in a deeper, lower resolution survey. The galaxies in the deeper survey do not even need to appear individually in the shallow survey. We give a toy model example to illustrate tradeoffs and considerations for applying this method. This approach will allow deep imaging surveys to leverage the high resolution of spectroscopic and narrow/medium band surveys underway, even when the latter do not have the same reach to high redshift.
Photometric redshifts (photo-zs) are fundamental in galaxy surveys to address different topics, from gravitational lensing and dark matter distribution to galaxy evolution. The Kilo Degree Survey (KiDS), i.e. the ESO public survey on the VLT Survey Telescope (VST), provides the unprecedented opportunity to exploit a large galaxy dataset with an exceptional image quality and depth in the optical wavebands. Using a KiDS subset of about 25,000 galaxies with measured spectroscopic redshifts, we have derived photo-zs using i) three different empirical methods based on supervised machine learning, ii) the Bayesian Photometric Redshift model (or BPZ), and iii) a classical SED template fitting procedure (Le Phare). We confirm that, in the regions of the photometric parameter space properly sampled by the spectroscopic templates, machine learning methods provide better redshift estimates, with a lower scatter and a smaller fraction of outliers. SED fitting techniques, however, provide useful information on the galaxy spectral type which can be effectively used to constrain systematic errors and to better characterize potential catastrophic outliers. Such classification is then used to specialize the training of regression machine learning models, by demonstrating that a hybrid approach, involving SED fitting and machine learning in a single collaborative framework, can be effectively used to improve the accuracy of photo-z estimates.
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